Castro, RodrigoRodrigoCastroElkin CárdenasWilly Sierra2025-08-252025-08-252020-07-1010.1016/j.jmaa.2020.1243812-s2.0-85087744073https://cris-uv-2.scimago.es/handle/123456789/3642WOS:000556890600039In this paper we present a Newton-type two-step method to approximate a solution of a nonlinear equation in Banach spaces. We establish a semilocal convergence theorem under Newton-Kantorovich-type conditions, both the convergence order and the efficiency index of the developed method are found. The iterative procedure presented here is a simple modification of the Newton-Kantorovich method, however, with the same number of function and derivative evaluations at each iteration, it is improved in two important aspects: Firstly, the convergence order is increased from 2 for the Newton-Kantorovich method to 1+2≈2.414 for the new method. Secondly, the efficiency index (convergence order per function evaluation) is improved from 2≈1.414 to (1+2)1/2≈1.553. We illustrate some of our results with a numerical example.enacceso restringidoAnalysisApplied MathematicsMathematicsMathematics, Appliedarticle